No Paul, Lee is indeed referring to the rate of discharge chart,
however, he has chosen the cut-off to be _*3 volts*_, rather than the
customary cut-off of_*2.5 volts*_. (No one uses a cut-off of 3 volts,
that I am aware of. All the charts note that 2.5v cut-off is the
standard for comparison. If we picked 3.5 volts as the cut-off, we would
get a huge spread in the apparent capacity, but that would be silly.)
You are correct that the 12 minute discharge (0.2C rate), the 0.5C rate,
and the 1C rate all show the same capacity, 3.25 mA-hr. While the 2 hour
discharge (2C rate) shows a slightly elevated capacity of 3.350 mA.
I suspect that the faster rates had some unavoidable internal
heating, (even though the case temperature was held at a constant 25
degrees Celsius,) which tends to decrease the internal resistance, and
tends to raise the terminal voltage under load, especially when the
impedance rises near the end. Thus, the apparent capacity shift is quite
likely due to increased internal temperature rather than ion diffusion.
Lead acid curves would have shown a much greater sensitivity to the
discharge rate. Much greater. As I said earlier, the ions can diffuse
perhaps 100 times more quickly in Li-Ion cells than in lead-acid cells,
which makes the Puekert exponent very close to unity in Li_ion. Puekert
is not really useful in Li_ion because the diffusion is so fast in Li-Ion.
Bill D.
On 3/17/2019 12:40 AM, paul dove via EV wrote:
That’s not what the spec sheet says. You are reading the graph for
temperature variations. There is almost no difference due to discharge
rates. 2C is 3250 and 0.5C is 3350 according to your spec sheet.
And lead acid batteries have a Puekert coefficient as low as 1.08.
Sent from my iPhone
On Mar 15, 2019, at 9:14 AM, Steve Heath via EV <[email protected]>
wrote:
Peukert's law is not an actual law but an empirical formula that is
based on actual physical measurements. It gives an approximate estimate of
how much capacity can be obtained. The way that it is used is that the
capacity is measured at different discharge rates to give a co-efficient
that can then be applied to other batteries. This is where the difficulty
lies. The coefficient is taken by measurement and providing another battery
is the same then the coefficient is applicable. If not and it isn't.
The key point is that the discharge curves for li ion batteries do vary
significantly depending on the load in real life according to the
manufacturer data. At the 0% soc end point, the capacities are the same
(give or take). This is why the Peukerts coefficient is close to 1 rather
than 1.2 or higher for a lead acid battery. Hence the comment that it is
not applicable. It is there but very small to be accurate. However at a
typical self preservation point e.g cutoff voltage used by BMS, the
capacities are different. As a result, there is a "Peukerts" effect where
the amount of capacity that can be obtained is different depending on the
discharge current. It is not the same Peukerts effect but the end result is
the same. Discharge more, less capacity...
The data sheet for a Panasonic 18650 shows this effect very well (
https://www.batteryspace.com/prod-specs/NCR18650B.pdf ) where a cut off
voltage of 3v gives a capacity of 2400mAh at 2c and 3300 mAh at 0.2C . At
the 0% soc point they all come out at 3300 and 3400. So discharging to 0%
soc, the discharge current is more or less irrelevant. Interestingly these
results are taken at constant cell temperature where any overheating
advantage is not applicable. Without seeing the complete paper that was
referred to, it is difficult to know if any comparison with manufacturer
data was made or whether tests were done at constant temperature and what
the results were.
Discharging to a lower 15-20% level to protect the battery, there is a
big difference. If you want to get the best capacity out of a li ion
battery with a BMS, either reduce the discharge rate or change the BMS to
accept a lower cutoff voltage and risk battery damage.
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